Is three dimensional supergravity dynamical?

Question

So it is well known that standard $D = 3$ Einstein gravity is non-dynamical in the sense that the graviton has no on-shell degrees of freedom (d.o.f $= D(D-3)/2$ and the theory is topological).

However, I have also seen that there are various theories of supergravity with up to $mathcal{N} = 16$ supersymmetries in $D = 3$. Are any of these theories dynamical (with a massless graviton), and if so, how?

alexarvanitakis · Accepted Answer

No; which is to say, the 3D SUGRAS most closely analogous to pure Einstein gravity in three dimensions are also topological in the sense you mention.
In fact the original reference that showed 3D gravity can be formulated as a Chern-Simons theory actually treated 3D supergravity! (Achucarro & Townsend https://inspirehep.net/literature/21208)

Is three dimensional supergravity dynamical?

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